Using multinomial logistic regression for multiple related outcomes Is it common practice (and adequate) to regroup two binary dependant variables into a single 4-level dependent variable to take advantage of the multinomial regression? For instance, say we have information on two related conditions (outcomes) A and B. A new 4-category variable would be defined such that:
category 1 = Neither conditions A nor B
category 2 = Condition A (only)
category 3 = Condition B (only)
category 4 = Both conditions A and B

This allows running a single multinomial regression instead of using two binary logistic models that include the same predictors.
 A: As @Riaz Rizvi suggests, this may not be a good idea.  
Your scheme enforces a particular (and rather unlikely) covariance structure on the problem by flattening to a multinomial this way.  Since you suspect, or at least wish to allow the possibility that the presence of A is informative of B, then you should be working with a bivariate probit.  Working with two separate logistic models is not going to be able to represent this.  The model is a regression  with an explicit correlated bivariate latent variable generating the choice probabilities, as discussed briefly in the link and at greater length in good econometrics texts.
A: A multinomial is perfectly fine in this situation, but it comes at two costs:


*

*An explosion in the number of parameters. (If you were to combine $n$ binary variables like this, you would have $2^n$ parameters instead of the original $n$.)

*The solution is harder to interpret if the original variables are actually independent.  (If you would have had a simple relationship such that input variable $x$ implies dependent variable $y=1$, you would now have $x$ implies that the combined dependent variable takes on one of the many outcomes corresponding to $y=1$.)


The major advantage is that your model can use the additional parameters to encode distributions not possible in the original model.
A: I don't think so. The multinomial distribution is derived from n independent variables, but your situation has two dependent variables. A multinomial regression is not applicable here. 
